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Two Trees


We solve a model with two “Lucas trees.” Each tree has i.i.d. dividend growth. The investor has log utility and consumes the sum of the two trees’ dividends. This model produces interesting asset-pricing dynamics, despite its simple ingredients. Investors want to rebalance their portfolios after any change in value. Since the size of the trees is fixed, however, prices must adjust to offset this desire. As a result, expected returns, excess returns, and return volatility all vary through time. Returns display serial correlation, and are predictable from price-dividend ratios in the time series and in the cross section. Return volatility can be greater than the volatility of cash flows, giving the appearance of “excess volatility.” Returns can be cross-correlated even when the cash flows are independent, giving the appearance of “contagion” or “spurious comovement.”

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